Some occupational therapists will teach Handwriting Without Tears. Am I right in understanding that your son is 6? I would not suggest going further with the Sylvan Center based on the what you've described above. She just doesn't have the background in gifted students to be able to assess him. In a normally developing child, a vision issue might result in below grade level reading. With a giftie, though, that is not necessarily true. They could be performing above grade level and still be having issues that prevent them from reaching their full potential. This is why so many 2E kids don't get support for their disabilities at school: because you have to fall behind to be recognized as having a problem. Their giftedness essentially hides their LD.
That said, if your son is 6 and was assessed at a 2nd grade writing level, that is still advanced. Perhaps not as advanced as other areas, but still above grade level. And a 6 year old may just not be physically ready to meet the handwriting expectations of an older child even if he is there intellectually. Sloppiness of handwriting is not necessarily related to sloppiness of organization or thought. It's just that pesky asynchrony where his hands are 6 year old hands but is thoughts are several grades ahead of that.
I would suggest an assessment by an OT (they often do free screenings) if you are concerned that he is delayed. They will compare him to his age peers with regard to fine motor skills. When I had my kindergartner assessed, the OT actually told me that the educational expectations of young children are often not even developmentally appropriate. For most kids at that age, for example, even writing lower case letters is a stretch.
And honestly,IMO, in this day and age, any teacher who would seriously grade down because of penmenship is out of touch with reality. Even now, elementary school is virtually the only place where anyone WRITES anything.